A load weighing 0.25 kg vibrates on a spring with a stiffness of 100 N / m.

A load weighing 0.25 kg vibrates on a spring with a stiffness of 100 N / m. what is its oscillation period? How long does it take 10 vibrations? A 9.86 kg load vibrates on a spring with a period of 2 s. What is the stiffness of the spring? What is the vibration frequency of the load?

First task.
Given: m = 0.25 kg;
K = 100 N / m;
n = 10.
Find: T, t.
Decision:
We use this formula:
T = 2n * root of m / k.
Substitute the values.
T = 6.28 * root of 0.25 / 100 = 6.28 * 0.05 = 0.314 s.
Then we find t. t = Tn.
We substitute the values there:
t = 10 * 0.314 = 3.14 s.
Answer: T = 0.314 s; t = 3.14 s.

Second task.
Given:
m = 9.86 kg;
T = 2s.
Find: k and spring stiffness (g)
Decision:
We use the formula and immediately substitute the values into it: k = 4 n ^ 2 m / T ^ 2 = 40 * 9.86 / 4 = 98.6.
Let’s find the stiffness.
w = 1 / T. That is, we get w = 1/2 = 0.5 Hz.
Answer: k = 98.6; w = 0.5 Hz